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Math Help - differentiable function of 3 variables

  1. #1
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    differentiable function of 3 variables

    If someone can help, please do help me for this question. I got stuck with it since yesterdays.

    Prove that if f is a differentiable function of 3 variables and g(x,y,z) = f(x-y, y-z, z-x), then gsubx(x,y,z) + gsuby(x,y,z) +gsubz(x,y,z)=0.

    Hint Let u =x-y, v=y-z, w=z-x, and write g(x,y,z)=f(u(x,y,z), v(x,y,z), w(x,y,z))

    Thank you very much.
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  2. #2
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    Quote Originally Posted by littlemu View Post
    If someone can help, please do help me for this question. I got stuck with it since yesterdays.

    Prove that if f is a differentiable function of 3 variables and g(x,y,z) = f(x-y, y-z, z-x), then gsubx(x,y,z) + gsuby(x,y,z) +gsubz(x,y,z)=0.

    Hint Let u =x-y, v=y-z, w=z-x, and write g(x,y,z)=f(u(x,y,z), v(x,y,z), w(x,y,z))

    Thank you very much.
    You have,
    g(u,v,w) with u=x-y and v=y-z and w=z-x

    Now you can use the Chain Rule.
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